assign = name

If given the option assign = x, where x is any name, IdentifySmallGroup will assign the isomorphism mapping $G$ to $H$ to the name x. This isomorphism can be used in the same way as the isomorphisms assigned by AreIsomorphic.

If x already has a value, then it needs to be protected from evaluation using quotation marks.

form = fpgroup or form = permgroup

This option can be used together with the assign option, explained above, in order to specify the form of the group $H$ that is the codomain of the isomorphism to be assigned to the name specified in the assign option.

Specifying form = fpgroup results in the codomain being a finitely presented group. Specifying form = permgroup (the default) results in the codomain being a permutation group. You can equivalently specify the string forms of these values, as form = "fpgroup" or form = "permgroup".

If no assign option is specified, then the form option is ignored.

The command IdentifySmallGroup finds if a group $H$ isomorphic to $G$ occurs in the small groups database. (Currently, that means that the order of the group is at most 511.) If so, it returns the numbers under which $H$ occurs in the database.

The value returned is a sequence of two numbers such that calling SmallGroup with those two numbers as arguments returns the group $H$.  The first number is the order of $G$.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$\mathrm{IdentifySmallGroup}\left(\mathrm{PSL}\left(3\,2\right)\right)$

$168,42$

$\mathrm{IdentifySmallGroup}\left(\mathrm{PSL}\left(2\,7\right)\right)$

$168,42$

$\mathrm{g1}≔\mathrm{SmallGroup}\left(96\,7\right)$

$\mathrm{g1}≔⟨\left(1\,2\right)\left(3\,21\right)\left(4\,30\right)\left(5\,15\right)\left(6\,14\right)\left(7\,17\right)\left(8\,16\right)\left(9\,18\right)\left(10\,20\right)\left(11\,19\right)\left(12\,23\right)\left(13\,27\right)\left(22\,51\right)\left(24\,47\right)\left(25\,46\right)\left(26\,52\right)\left(28\,66\right)\left(29\,65\right)\left(31\,45\right)\left(32\,48\right)\left(33\,80\right)\left(34\,79\right)\left(35\,58\right)\left(36\,57\right)\left(37\,56\right)\left(38\,55\right)\left(39\,62\right)\left(40\,61\right)\left(41\,60\right)\left(42\,59\right)\left(43\,64\right)\left(44\,63\right)\left(49\,70\right)\left(50\,69\right)\left(53\,78\right)\left(54\,77\right)\left(67\,94\right)\left(68\,93\right)\left(71\,90\right)\left(72\,89\right)\left(73\,88\right)\left(74\,87\right)\left(75\,96\right)\left(76\,95\right)\left(81\,86\right)\left(82\,85\right)\left(83\,92\right)\left(84\,91\right)\,\left(1\,3\,22\,32\,8\,26\,5\,23\,9\,27\,6\,24\,7\,25\,31\,4\right)\left(2\,12\,45\,52\,17\,48\,14\,21\,18\,30\,15\,46\,16\,47\,51\,13\right)\left(10\,28\,67\,83\,41\,75\,35\,69\,43\,77\,37\,71\,39\,73\,81\,33\right)\left(11\,29\,68\,84\,42\,76\,36\,70\,44\,78\,38\,72\,40\,74\,82\,34\right)\left(19\,49\,85\,95\,61\,91\,55\,65\,63\,79\,57\,87\,59\,89\,93\,53\right)\left(20\,50\,86\,96\,62\,92\,56\,66\,64\,80\,58\,88\,60\,90\,94\,54\right)\,\left(1\,5\,7\,22\,9\,31\,8\,6\right)\left(2\,14\,16\,45\,18\,51\,17\,15\right)\left(3\,23\,25\,32\,27\,4\,26\,24\right)\left(10\,35\,39\,67\,43\,81\,41\,37\right)\left(11\,36\,40\,68\,44\,82\,42\,38\right)\left(12\,21\,47\,52\,30\,13\,48\,46\right)\left(19\,55\,59\,85\,63\,93\,61\,57\right)\left(20\,56\,60\,86\,64\,94\,62\,58\right)\left(28\,69\,73\,83\,77\,33\,75\,71\right)\left(29\,70\,74\,84\,78\,34\,76\,72\right)\left(49\,65\,89\,95\,79\,53\,91\,87\right)\left(50\,66\,90\,96\,80\,54\,92\,88\right)\,\left(1\,7\,9\,8\right)\left(2\,16\,18\,17\right)\left(3\,25\,27\,26\right)\left(4\,24\,23\,32\right)\left(5\,22\,31\,6\right)\left(10\,39\,43\,41\right)\left(11\,40\,44\,42\right)\left(12\,47\,30\,48\right)\left(13\,46\,21\,52\right)\left(14\,45\,51\,15\right)\left(19\,59\,63\,61\right)\left(20\,60\,64\,62\right)\left(28\,73\,77\,75\right)\left(29\,74\,78\,76\right)\left(33\,71\,69\,83\right)\left(34\,72\,70\,84\right)\left(35\,67\,81\,37\right)\left(36\,68\,82\,38\right)\left(49\,89\,79\,91\right)\left(50\,90\,80\,92\right)\left(53\,87\,65\,95\right)\left(54\,88\,66\,96\right)\left(55\,85\,93\,57\right)\left(56\,86\,94\,58\right)\,\left(1\,9\right)\left(2\,18\right)\left(3\,27\right)\left(4\,23\right)\left(5\,31\right)\left(6\,22\right)\left(7\,8\right)\left(10\,43\right)\left(11\,44\right)\left(12\,30\right)\left(13\,21\right)\left(14\,51\right)\left(15\,45\right)\left(16\,17\right)\left(19\,63\right)\left(20\,64\right)\left(24\,32\right)\left(25\,26\right)\left(28\,77\right)\left(29\,78\right)\left(33\,69\right)\left(34\,70\right)\left(35\,81\right)\left(36\,82\right)\left(37\,67\right)\left(38\,68\right)\left(39\,41\right)\left(40\,42\right)\left(46\,52\right)\left(47\,48\right)\left(49\,79\right)\left(50\,80\right)\left(53\,65\right)\left(54\,66\right)\left(55\,93\right)\left(56\,94\right)\left(57\,85\right)\left(58\,86\right)\left(59\,61\right)\left(60\,62\right)\left(71\,83\right)\left(72\,84\right)\left(73\,75\right)\left(74\,76\right)\left(87\,95\right)\left(88\,96\right)\left(89\,91\right)\left(90\,92\right)\,\left(1\,10\,11\right)\left(2\,19\,20\right)\left(3\,28\,29\right)\left(4\,33\,34\right)\left(5\,35\,36\right)\left(6\,37\,38\right)\left(7\,39\,40\right)\left(8\,41\,42\right)\left(9\,43\,44\right)\left(12\,49\,50\right)\left(13\,53\,54\right)\left(14\,55\,56\right)\left(15\,57\,58\right)\left(16\,59\,60\right)\left(17\,61\,62\right)\left(18\,63\,64\right)\left(21\,65\,66\right)\left(22\,67\,68\right)\left(23\,69\,70\right)\left(24\,71\,72\right)\left(25\,73\,74\right)\left(26\,75\,76\right)\left(27\,77\,78\right)\left(30\,79\,80\right)\left(31\,81\,82\right)\left(32\,83\,84\right)\left(45\,85\,86\right)\left(46\,87\,88\right)\left(47\,89\,90\right)\left(48\,91\,92\right)\left(51\,93\,94\right)\left(52\,95\,96\right)⟩$

$\mathrm{g2}≔\mathrm{CayleyTableGroup}\left(\mathrm{g1}\right)$

$\mathrm{g2}≔\mathrm{<\; a\; Cayley\; table\; group\; with\; 96\; elements\; >}$

$\mathrm{IdentifySmallGroup}\left(\mathrm{g2}\&comma;'\mathrm{assign}=\mathrm{iso}'\right)$

$96,7$

$\mathrm{Domain}\left(\mathrm{iso}\right)$

$\mathrm{<\; a\; Cayley\; table\; group\; with\; 96\; elements\; >}$

$\mathrm{Codomain}\left(\mathrm{iso}\right)$

$⟨\left(1\&comma;2\right)\left(3\&comma;21\right)\left(4\&comma;30\right)\left(5\&comma;15\right)\left(6\&comma;14\right)\left(7\&comma;17\right)\left(8\&comma;16\right)\left(9\&comma;18\right)\left(10\&comma;20\right)\left(11\&comma;19\right)\left(12\&comma;23\right)\left(13\&comma;27\right)\left(22\&comma;51\right)\left(24\&comma;47\right)\left(25\&comma;46\right)\left(26\&comma;52\right)\left(28\&comma;66\right)\left(29\&comma;65\right)\left(31\&comma;45\right)\left(32\&comma;48\right)\left(33\&comma;80\right)\left(34\&comma;79\right)\left(35\&comma;58\right)\left(36\&comma;57\right)\left(37\&comma;56\right)\left(38\&comma;55\right)\left(39\&comma;62\right)\left(40\&comma;61\right)\left(41\&comma;60\right)\left(42\&comma;59\right)\left(43\&comma;64\right)\left(44\&comma;63\right)\left(49\&comma;70\right)\left(50\&comma;69\right)\left(53\&comma;78\right)\left(54\&comma;77\right)\left(67\&comma;94\right)\left(68\&comma;93\right)\left(71\&comma;90\right)\left(72\&comma;89\right)\left(73\&comma;88\right)\left(74\&comma;87\right)\left(75\&comma;96\right)\left(76\&comma;95\right)\left(81\&comma;86\right)\left(82\&comma;85\right)\left(83\&comma;92\right)\left(84\&comma;91\right)\&comma;\left(1\&comma;3\&comma;22\&comma;32\&comma;8\&comma;26\&comma;5\&comma;23\&comma;9\&comma;27\&comma;6\&comma;24\&comma;7\&comma;25\&comma;31\&comma;4\right)\left(2\&comma;12\&comma;45\&comma;52\&comma;17\&comma;48\&comma;14\&comma;21\&comma;18\&comma;30\&comma;15\&comma;46\&comma;16\&comma;47\&comma;51\&comma;13\right)\left(10\&comma;28\&comma;67\&comma;83\&comma;41\&comma;75\&comma;35\&comma;69\&comma;43\&comma;77\&comma;37\&comma;71\&comma;39\&comma;73\&comma;81\&comma;33\right)\left(11\&comma;29\&comma;68\&comma;84\&comma;42\&comma;76\&comma;36\&comma;70\&comma;44\&comma;78\&comma;38\&comma;72\&comma;40\&comma;74\&comma;82\&comma;34\right)\left(19\&comma;49\&comma;85\&comma;95\&comma;61\&comma;91\&comma;55\&comma;65\&comma;63\&comma;79\&comma;57\&comma;87\&comma;59\&comma;89\&comma;93\&comma;53\right)\left(20\&comma;50\&comma;86\&comma;96\&comma;62\&comma;92\&comma;56\&comma;66\&comma;64\&comma;80\&comma;58\&comma;88\&comma;60\&comma;90\&comma;94\&comma;54\right)\&comma;\left(1\&comma;5\&comma;7\&comma;22\&comma;9\&comma;31\&comma;8\&comma;6\right)\left(2\&comma;14\&comma;16\&comma;45\&comma;18\&comma;51\&comma;17\&comma;15\right)\left(3\&comma;23\&comma;25\&comma;32\&comma;27\&comma;4\&comma;26\&comma;24\right)\left(10\&comma;35\&comma;39\&comma;67\&comma;43\&comma;81\&comma;41\&comma;37\right)\left(11\&comma;36\&comma;40\&comma;68\&comma;44\&comma;82\&comma;42\&comma;38\right)\left(12\&comma;21\&comma;47\&comma;52\&comma;30\&comma;13\&comma;48\&comma;46\right)\left(19\&comma;55\&comma;59\&comma;85\&comma;63\&comma;93\&comma;61\&comma;57\right)\left(20\&comma;56\&comma;60\&comma;86\&comma;64\&comma;94\&comma;62\&comma;58\right)\left(28\&comma;69\&comma;73\&comma;83\&comma;77\&comma;33\&comma;75\&comma;71\right)\left(29\&comma;70\&comma;74\&comma;84\&comma;78\&comma;34\&comma;76\&comma;72\right)\left(49\&comma;65\&comma;89\&comma;95\&comma;79\&comma;53\&comma;91\&comma;87\right)\left(50\&comma;66\&comma;90\&comma;96\&comma;80\&comma;54\&comma;92\&comma;88\right)\&comma;\left(1\&comma;7\&comma;9\&comma;8\right)\left(2\&comma;16\&comma;18\&comma;17\right)\left(3\&comma;25\&comma;27\&comma;26\right)\left(4\&comma;24\&comma;23\&comma;32\right)\left(5\&comma;22\&comma;31\&comma;6\right)\left(10\&comma;39\&comma;43\&comma;41\right)\left(11\&comma;40\&comma;44\&comma;42\right)\left(12\&comma;47\&comma;30\&comma;48\right)\left(13\&comma;46\&comma;21\&comma;52\right)\left(14\&comma;45\&comma;51\&comma;15\right)\left(19\&comma;59\&comma;63\&comma;61\right)\left(20\&comma;60\&comma;64\&comma;62\right)\left(28\&comma;73\&comma;77\&comma;75\right)\left(29\&comma;74\&comma;78\&comma;76\right)\left(33\&comma;71\&comma;69\&comma;83\right)\left(34\&comma;72\&comma;70\&comma;84\right)\left(35\&comma;67\&comma;81\&comma;37\right)\left(36\&comma;68\&comma;82\&comma;38\right)\left(49\&comma;89\&comma;79\&comma;91\right)\left(50\&comma;90\&comma;80\&comma;92\right)\left(53\&comma;87\&comma;65\&comma;95\right)\left(54\&comma;88\&comma;66\&comma;96\right)\left(55\&comma;85\&comma;93\&comma;57\right)\left(56\&comma;86\&comma;94\&comma;58\right)\&comma;\left(1\&comma;9\right)\left(2\&comma;18\right)\left(3\&comma;27\right)\left(4\&comma;23\right)\left(5\&comma;31\right)\left(6\&comma;22\right)\left(7\&comma;8\right)\left(10\&comma;43\right)\left(11\&comma;44\right)\left(12\&comma;30\right)\left(13\&comma;21\right)\left(14\&comma;51\right)\left(15\&comma;45\right)\left(16\&comma;17\right)\left(19\&comma;63\right)\left(20\&comma;64\right)\left(24\&comma;32\right)\left(25\&comma;26\right)\left(28\&comma;77\right)\left(29\&comma;78\right)\left(33\&comma;69\right)\left(34\&comma;70\right)\left(35\&comma;81\right)\left(36\&comma;82\right)\left(37\&comma;67\right)\left(38\&comma;68\right)\left(39\&comma;41\right)\left(40\&comma;42\right)\left(46\&comma;52\right)\left(47\&comma;48\right)\left(49\&comma;79\right)\left(50\&comma;80\right)\left(53\&comma;65\right)\left(54\&comma;66\right)\left(55\&comma;93\right)\left(56\&comma;94\right)\left(57\&comma;85\right)\left(58\&comma;86\right)\left(59\&comma;61\right)\left(60\&comma;62\right)\left(71\&comma;83\right)\left(72\&comma;84\right)\left(73\&comma;75\right)\left(74\&comma;76\right)\left(87\&comma;95\right)\left(88\&comma;96\right)\left(89\&comma;91\right)\left(90\&comma;92\right)\&comma;\left(1\&comma;10\&comma;11\right)\left(2\&comma;19\&comma;20\right)\left(3\&comma;28\&comma;29\right)\left(4\&comma;33\&comma;34\right)\left(5\&comma;35\&comma;36\right)\left(6\&comma;37\&comma;38\right)\left(7\&comma;39\&comma;40\right)\left(8\&comma;41\&comma;42\right)\left(9\&comma;43\&comma;44\right)\left(12\&comma;49\&comma;50\right)\left(13\&comma;53\&comma;54\right)\left(14\&comma;55\&comma;56\right)\left(15\&comma;57\&comma;58\right)\left(16\&comma;59\&comma;60\right)\left(17\&comma;61\&comma;62\right)\left(18\&comma;63\&comma;64\right)\left(21\&comma;65\&comma;66\right)\left(22\&comma;67\&comma;68\right)\left(23\&comma;69\&comma;70\right)\left(24\&comma;71\&comma;72\right)\left(25\&comma;73\&comma;74\right)\left(26\&comma;75\&comma;76\right)\left(27\&comma;77\&comma;78\right)\left(30\&comma;79\&comma;80\right)\left(31\&comma;81\&comma;82\right)\left(32\&comma;83\&comma;84\right)\left(45\&comma;85\&comma;86\right)\left(46\&comma;87\&comma;88\right)\left(47\&comma;89\&comma;90\right)\left(48\&comma;91\&comma;92\right)\left(51\&comma;93\&comma;94\right)\left(52\&comma;95\&comma;96\right)⟩$

$\mathrm{infolevel}\left[\mathrm{GroupTheory}\right]≔3$

${\mathrm{infolevel}}_{\mathrm{GroupTheory}}≔3$

$\mathrm{g3}≔\mathrm{SmallGroup}\left(128\&comma;1607\right)$

$\mathrm{g3}≔⟨\left(1\&comma;2\&comma;8\&comma;16\&comma;11\&comma;18\&comma;9\&comma;3\right)\left(4\&comma;24\&comma;28\&comma;19\&comma;30\&comma;12\&comma;29\&comma;25\right)\left(5\&comma;31\&comma;35\&comma;20\&comma;37\&comma;13\&comma;36\&comma;32\right)\left(6\&comma;14\&comma;39\&comma;56\&comma;42\&comma;58\&comma;40\&comma;21\right)\left(7\&comma;15\&comma;44\&comma;60\&comma;47\&comma;62\&comma;45\&comma;22\right)\left(10\&comma;17\&comma;48\&comma;63\&comma;50\&comma;64\&comma;49\&comma;23\right)\left(26\&comma;73\&comma;78\&comma;65\&comma;80\&comma;51\&comma;79\&comma;75\right)\left(27\&comma;74\&comma;82\&comma;66\&comma;84\&comma;52\&comma;83\&comma;76\right)\left(33\&comma;85\&comma;90\&comma;67\&comma;92\&comma;53\&comma;91\&comma;87\right)\left(34\&comma;86\&comma;94\&comma;68\&comma;96\&comma;54\&comma;95\&comma;88\right)\left(38\&comma;55\&comma;97\&comma;71\&comma;43\&comma;59\&comma;98\&comma;69\right)\left(41\&comma;57\&comma;100\&comma;112\&comma;102\&comma;113\&comma;101\&comma;70\right)\left(46\&comma;61\&comma;104\&comma;115\&comma;106\&comma;116\&comma;105\&comma;72\right)\left(77\&comma;108\&comma;123\&comma;117\&comma;81\&comma;107\&comma;124\&comma;118\right)\left(89\&comma;110\&comma;125\&comma;119\&comma;93\&comma;109\&comma;126\&comma;120\right)\left(99\&comma;111\&comma;127\&comma;122\&comma;103\&comma;114\&comma;128\&comma;121\right)\&comma;\left(1\&comma;4\&comma;10\&comma;5\right)\left(2\&comma;12\&comma;17\&comma;13\right)\left(3\&comma;19\&comma;23\&comma;20\right)\left(6\&comma;26\&comma;41\&comma;33\right)\left(7\&comma;27\&comma;46\&comma;34\right)\left(8\&comma;28\&comma;48\&comma;35\right)\left(9\&comma;29\&comma;49\&comma;36\right)\left(11\&comma;30\&comma;50\&comma;37\right)\left(14\&comma;51\&comma;57\&comma;53\right)\left(15\&comma;52\&comma;61\&comma;54\right)\left(16\&comma;25\&comma;63\&comma;32\right)\left(18\&comma;24\&comma;64\&comma;31\right)\left(21\&comma;65\&comma;70\&comma;67\right)\left(22\&comma;66\&comma;72\&comma;68\right)\left(38\&comma;77\&comma;99\&comma;89\right)\left(39\&comma;78\&comma;100\&comma;90\right)\left(40\&comma;79\&comma;101\&comma;91\right)\left(42\&comma;80\&comma;102\&comma;92\right)\left(43\&comma;81\&comma;103\&comma;93\right)\left(44\&comma;82\&comma;104\&comma;94\right)\left(45\&comma;83\&comma;105\&comma;95\right)\left(47\&comma;84\&comma;106\&comma;96\right)\left(55\&comma;107\&comma;111\&comma;109\right)\left(56\&comma;75\&comma;112\&comma;87\right)\left(58\&comma;73\&comma;113\&comma;85\right)\left(59\&comma;108\&comma;114\&comma;110\right)\left(60\&comma;76\&comma;115\&comma;88\right)\left(62\&comma;74\&comma;116\&comma;86\right)\left(69\&comma;117\&comma;121\&comma;119\right)\left(71\&comma;118\&comma;122\&comma;120\right)\left(97\&comma;123\&comma;127\&comma;125\right)\left(98\&comma;124\&comma;128\&comma;126\right)\&comma;\left(1\&comma;6\right)\left(2\&comma;14\right)\left(3\&comma;21\right)\left(4\&comma;26\right)\left(5\&comma;33\right)\left(7\&comma;43\right)\left(8\&comma;39\right)\left(9\&comma;40\right)\left(10\&comma;41\right)\left(11\&comma;42\right)\left(12\&comma;51\right)\left(13\&comma;53\right)\left(15\&comma;59\right)\left(16\&comma;56\right)\left(17\&comma;57\right)\left(18\&comma;58\right)\left(19\&comma;65\right)\left(20\&comma;67\right)\left(22\&comma;71\right)\left(23\&comma;70\right)\left(24\&comma;73\right)\left(25\&comma;75\right)\left(27\&comma;81\right)\left(28\&comma;78\right)\left(29\&comma;79\right)\left(30\&comma;80\right)\left(31\&comma;85\right)\left(32\&comma;87\right)\left(34\&comma;93\right)\left(35\&comma;90\right)\left(36\&comma;91\right)\left(37\&comma;92\right)\left(38\&comma;47\right)\left(44\&comma;98\right)\left(45\&comma;97\right)\left(46\&comma;103\right)\left(48\&comma;100\right)\left(49\&comma;101\right)\left(50\&comma;102\right)\left(52\&comma;108\right)\left(54\&comma;110\right)\left(55\&comma;62\right)\left(60\&comma;69\right)\left(61\&comma;114\right)\left(63\&comma;112\right)\left(64\&comma;113\right)\left(66\&comma;118\right)\left(68\&comma;120\right)\left(72\&comma;122\right)\left(74\&comma;107\right)\left(76\&comma;117\right)\left(77\&comma;84\right)\left(82\&comma;124\right)\left(83\&comma;123\right)\left(86\&comma;109\right)\left(88\&comma;119\right)\left(89\&comma;96\right)\left(94\&comma;126\right)\left(95\&comma;125\right)\left(99\&comma;106\right)\left(104\&comma;128\right)\left(105\&comma;127\right)\left(111\&comma;116\right)\left(115\&comma;121\right)\&comma;\left(1\&comma;7\right)\left(2\&comma;15\right)\left(3\&comma;22\right)\left(4\&comma;27\right)\left(5\&comma;34\right)\left(6\&comma;38\right)\left(8\&comma;44\right)\left(9\&comma;45\right)\left(10\&comma;46\right)\left(11\&comma;47\right)\left(12\&comma;52\right)\left(13\&comma;54\right)\left(14\&comma;55\right)\left(16\&comma;60\right)\left(17\&comma;61\right)\left(18\&comma;62\right)\left(19\&comma;66\right)\left(20\&comma;68\right)\left(21\&comma;69\right)\left(23\&comma;72\right)\left(24\&comma;74\right)\left(25\&comma;76\right)\left(26\&comma;77\right)\left(28\&comma;82\right)\left(29\&comma;83\right)\left(30\&comma;84\right)\left(31\&comma;86\right)\left(32\&comma;88\right)\left(33\&comma;89\right)\left(35\&comma;94\right)\left(36\&comma;95\right)\left(37\&comma;96\right)\left(39\&comma;97\right)\left(40\&comma;98\right)\left(41\&comma;99\right)\left(42\&comma;43\right)\left(48\&comma;104\right)\left(49\&comma;105\right)\left(50\&comma;106\right)\left(51\&comma;107\right)\left(53\&comma;109\right)\left(56\&comma;71\right)\left(57\&comma;111\right)\left(58\&comma;59\right)\left(63\&comma;115\right)\left(64\&comma;116\right)\left(65\&comma;117\right)\left(67\&comma;119\right)\left(70\&comma;121\right)\left(73\&comma;108\right)\left(75\&comma;118\right)\left(78\&comma;123\right)\left(79\&comma;124\right)\left(80\&comma;81\right)\left(85\&comma;110\right)\left(87\&comma;120\right)\left(90\&comma;125\right)\left(91\&comma;126\right)\left(92\&comma;93\right)\left(100\&comma;127\right)\left(101\&comma;128\right)\left(102\&comma;103\right)\left(112\&comma;122\right)\left(113\&comma;114\right)\&comma;\left(1\&comma;8\&comma;11\&comma;9\right)\left(2\&comma;16\&comma;18\&comma;3\right)\left(4\&comma;28\&comma;30\&comma;29\right)\left(5\&comma;35\&comma;37\&comma;36\right)\left(6\&comma;39\&comma;42\&comma;40\right)\left(7\&comma;44\&comma;47\&comma;45\right)\left(10\&comma;48\&comma;50\&comma;49\right)\left(12\&comma;25\&comma;24\&comma;19\right)\left(13\&comma;32\&comma;31\&comma;20\right)\left(14\&comma;56\&comma;58\&comma;21\right)\left(15\&comma;60\&comma;62\&comma;22\right)\left(17\&comma;63\&comma;64\&comma;23\right)\left(26\&comma;78\&comma;80\&comma;79\right)\left(27\&comma;82\&comma;84\&comma;83\right)\left(33\&comma;90\&comma;92\&comma;91\right)\left(34\&comma;94\&comma;96\&comma;95\right)\left(38\&comma;97\&comma;43\&comma;98\right)\left(41\&comma;100\&comma;102\&comma;101\right)\left(46\&comma;104\&comma;106\&comma;105\right)\left(51\&comma;75\&comma;73\&comma;65\right)\left(52\&comma;76\&comma;74\&comma;66\right)\left(53\&comma;87\&comma;85\&comma;67\right)\left(54\&comma;88\&comma;86\&comma;68\right)\left(55\&comma;71\&comma;59\&comma;69\right)\left(57\&comma;112\&comma;113\&comma;70\right)\left(61\&comma;115\&comma;116\&comma;72\right)\left(77\&comma;123\&comma;81\&comma;124\right)\left(89\&comma;125\&comma;93\&comma;126\right)\left(99\&comma;127\&comma;103\&comma;128\right)\left(107\&comma;118\&comma;108\&comma;117\right)\left(109\&comma;120\&comma;110\&comma;119\right)\left(111\&comma;122\&comma;114\&comma;121\right)\&comma;\left(1\&comma;10\right)\left(2\&comma;17\right)\left(3\&comma;23\right)\left(4\&comma;5\right)\left(6\&comma;41\right)\left(7\&comma;46\right)\left(8\&comma;48\right)\left(9\&comma;49\right)\left(11\&comma;50\right)\left(12\&comma;13\right)\left(14\&comma;57\right)\left(15\&comma;61\right)\left(16\&comma;63\right)\left(18\&comma;64\right)\left(19\&comma;20\right)\left(21\&comma;70\right)\left(22\&comma;72\right)\left(24\&comma;31\right)\left(25\&comma;32\right)\left(26\&comma;33\right)\left(27\&comma;34\right)\left(28\&comma;35\right)\left(29\&comma;36\right)\left(30\&comma;37\right)\left(38\&comma;99\right)\left(39\&comma;100\right)\left(40\&comma;101\right)\left(42\&comma;102\right)\left(43\&comma;103\right)\left(44\&comma;104\right)\left(45\&comma;105\right)\left(47\&comma;106\right)\left(51\&comma;53\right)\left(52\&comma;54\right)\left(55\&comma;111\right)\left(56\&comma;112\right)\left(58\&comma;113\right)\left(59\&comma;114\right)\left(60\&comma;115\right)\left(62\&comma;116\right)\left(65\&comma;67\right)\left(66\&comma;68\right)\left(69\&comma;121\right)\left(71\&comma;122\right)\left(73\&comma;85\right)\left(74\&comma;86\right)\left(75\&comma;87\right)\left(76\&comma;88\right)\left(77\&comma;89\right)\left(78\&comma;90\right)\left(79\&comma;91\right)\left(80\&comma;92\right)\left(81\&comma;93\right)\left(82\&comma;94\right)\left(83\&comma;95\right)\left(84\&comma;96\right)\left(97\&comma;127\right)\left(98\&comma;128\right)\left(107\&comma;109\right)\left(108\&comma;110\right)\left(117\&comma;119\right)\left(118\&comma;120\right)\left(123\&comma;125\right)\left(124\&comma;126\right)\&comma;\left(1\&comma;11\right)\left(2\&comma;18\right)\left(3\&comma;16\right)\left(4\&comma;30\right)\left(5\&comma;37\right)\left(6\&comma;42\right)\left(7\&comma;47\right)\left(8\&comma;9\right)\left(10\&comma;50\right)\left(12\&comma;24\right)\left(13\&comma;31\right)\left(14\&comma;58\right)\left(15\&comma;62\right)\left(17\&comma;64\right)\left(19\&comma;25\right)\left(20\&comma;32\right)\left(21\&comma;56\right)\left(22\&comma;60\right)\left(23\&comma;63\right)\left(26\&comma;80\right)\left(27\&comma;84\right)\left(28\&comma;29\right)\left(33\&comma;92\right)\left(34\&comma;96\right)\left(35\&comma;36\right)\left(38\&comma;43\right)\left(39\&comma;40\right)\left(41\&comma;102\right)\left(44\&comma;45\right)\left(46\&comma;106\right)\left(48\&comma;49\right)\left(51\&comma;73\right)\left(52\&comma;74\right)\left(53\&comma;85\right)\left(54\&comma;86\right)\left(55\&comma;59\right)\left(57\&comma;113\right)\left(61\&comma;116\right)\left(65\&comma;75\right)\left(66\&comma;76\right)\left(67\&comma;87\right)\left(68\&comma;88\right)\left(69\&comma;71\right)\left(70\&comma;112\right)\left(72\&comma;115\right)\left(77\&comma;81\right)\left(78\&comma;79\right)\left(82\&comma;83\right)\left(89\&comma;93\right)\left(90\&comma;91\right)\left(94\&comma;95\right)\left(97\&comma;98\right)\left(99\&comma;103\right)\left(100\&comma;101\right)\left(104\&comma;105\right)\left(107\&comma;108\right)\left(109\&comma;110\right)\left(111\&comma;114\right)\left(117\&comma;118\right)\left(119\&comma;120\right)\left(121\&comma;122\right)\left(123\&comma;124\right)\left(125\&comma;126\right)\left(127\&comma;128\right)⟩$

$\mathrm{IdentifySmallGroup}\left(\mathrm{g3}\right)$

$128,1607$

The GroupTheory[IdentifySmallGroup] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.